Drama CDs fall under media and media items must have a JAN/Catalog code on their database entries to be added (Doujinshi are the exception though.). It seems like your drama CD could be bundled with a game or something so it can't be split from the main media (a game etc. that has their own JAN/catalog code) either.

Just to add on, if you need help for identifying origins of items, you can ask in CLUB #99 too. :)

It's fine if it doesn't have any product code in it. You just gotta note down where it came from/what it came with and a link to the official japanese site that mentions the drama cd. Don't forget to put in the origin, company, voice actors, date of release, no. of tracks, etc.